Can we study warm dense matter using density matrix quantum Monte Carlo? A study of the sign problem and molecular hydrogen chains.

Finite temperature electronic energies play a role in understanding warm dense matter. The recently developed density matrix quantum Monte Carlo (DMQMC) method can be used to obtain exact-on-average finite temperature energies. The fermion sign problem exists for DMQMC much like the full configuration interaction quantum Monte Carlo method (FCIQMC), which it is related to. We perform a systematic study of the sign problem in DMQMC using Hn chains, where n = (4,6,8,10). This systematic study looks at a range of walker populations and the resulting energies for each system. In doing so, we probe the impact the sign problem has in DMQMC. We also investigate how the simulation variables and the sign problem are related by measuring the plateau heights of the hydrogen chains previously mentioned.